How to clean this flat shower head?

We just moved into a new house and have no idea how to clean this shower head. It is flush to the tile ceiling in the shower, and has a ton of rubber nozzles. Many of them are clogged with black residue. I am thinking that they need to soak in CLR, but I can’t do the bag & elastic band trick like I am used to doing with a normal shower head.

Help!